diff --git a/Lib/test/datetimetester.py b/Lib/test/datetimetester.py
--- a/Lib/test/datetimetester.py
+++ b/Lib/test/datetimetester.py
@@ -64,7 +64,7 @@
         self.assertEqual(dar(7, -3), -2)
         self.assertEqual(dar(-7, -3), 2)
 
-        # ties to even - eight cases: 
+        # ties to even - eight cases:
         # (2 signs of a) x (2 signs of b) x (even / odd quotient)
         self.assertEqual(dar(10, 4), 2)
         self.assertEqual(dar(-10, 4), -2)
@@ -76,7 +76,7 @@
         self.assertEqual(dar(6, -4), -2)
         self.assertEqual(dar(-6, -4), 2)
 
-        
+
 #############################################################################
 # tzinfo tests
 
diff --git a/Lib/test/test_time.py b/Lib/test/test_time.py
--- a/Lib/test/test_time.py
+++ b/Lib/test/test_time.py
@@ -489,6 +489,7 @@
 
 class _TestAsctimeYear:
     _format = '%d'
+    MINYEAR = TIME_MINYEAR
 
     def yearstr(self, y):
         return time.asctime((y,) + (0,) * 8).split()[-1]
@@ -509,6 +510,7 @@
         _format = '%04d'
     else:
         _format = '%d'
+    MINYEAR = TIME_MINYEAR + 1900
 
     def yearstr(self, y):
         return time.strftime('%Y', (y,) + (0,) * 8)
@@ -570,10 +572,7 @@
         self.assertEqual(self.yearstr(-123456789), str(-123456789))
         self.assertEqual(self.yearstr(-1234567890), str(-1234567890))
         self.assertEqual(self.yearstr(TIME_MINYEAR + 1900), str(TIME_MINYEAR + 1900))
-        # Issue #13312: it may return wrong value for year < TIME_MINYEAR + 1900
-        # Skip the value test, but check that no error is raised
-        self.yearstr(TIME_MINYEAR)
-        # self.assertEqual(self.yearstr(TIME_MINYEAR), str(TIME_MINYEAR))
+        self.assertEqual(self.yearstr(self.MINYEAR), str(self.MINYEAR))
         self.assertRaises(OverflowError, self.yearstr, TIME_MINYEAR - 1)
 
 
diff --git a/Modules/timemodule.c b/Modules/timemodule.c
--- a/Modules/timemodule.c
+++ b/Modules/timemodule.c
@@ -424,7 +424,7 @@
  * an exception and return 0 on error.
  */
 static int
-gettmarg(PyObject *args, struct tm *p)
+gettmarg(PyObject *args, struct tm *p, int tm_year_zero)
 {
     int y;
 
@@ -441,7 +441,7 @@
                           &p->tm_hour, &p->tm_min, &p->tm_sec,
                           &p->tm_wday, &p->tm_yday, &p->tm_isdst))
         return 0;
-    p->tm_year = y - 1900;
+    p->tm_year = y - tm_year_zero;
     p->tm_mon--;
     p->tm_wday = (p->tm_wday + 1) % 7;
     p->tm_yday--;
@@ -595,7 +595,7 @@
         if (pylocaltime(&tt, &buf) == -1)
             return NULL;
     }
-    else if (!gettmarg(tup, &buf) || !checktm(&buf))
+    else if (!gettmarg(tup, &buf, 1900) || !checktm(&buf))
         return NULL;
 
 #if defined(_MSC_VER) || defined(sun) || defined(_AIX)
@@ -768,7 +768,7 @@
         mon_name[timeptr->tm_mon],
         timeptr->tm_mday, timeptr->tm_hour,
         timeptr->tm_min, timeptr->tm_sec,
-        1900 + timeptr->tm_year);
+        timeptr->tm_year);
 }
 
 static PyObject *
@@ -784,7 +784,7 @@
         if (pylocaltime(&tt, &buf) == -1)
             return NULL;
 
-    } else if (!gettmarg(tup, &buf) || !checktm(&buf))
+    } else if (!gettmarg(tup, &buf, 0) || !checktm(&buf))
         return NULL;
     return _asctime(&buf);
 }
@@ -805,6 +805,7 @@
         return NULL;
     if (pylocaltime(&tt, &buf) == -1)
         return NULL;
+    buf.tm_year += 1900;
     return _asctime(&buf);
 }
 
@@ -821,7 +822,7 @@
 {
     struct tm buf;
     time_t tt;
-    if (!gettmarg(tup, &buf))
+    if (!gettmarg(tup, &buf, 1900))
         return NULL;
 #ifdef _AIX
     /* year < 1902 or year > 2037 */